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Space Sci Rev (2010) 154: 57–77DOI 10.1007/s11214-010-9689-0
Deriving the Absolute Reflectance of Lunar SurfaceUsing SELENE (Kaguya) Multiband Imager Data
Makiko Ohtake · Tsuneo Matsunaga · Yasuhiro Yokota · Satoru Yamamoto ·Yoshiko Ogawa · Tomokatsu Morota · Chikatoshi Honda · Junichi Haruyama ·Kouhei Kitazato · Hiroshi Takeda · Akira Iwasaki · Ryousuke Nakamura ·Takahiro Hiroi · Sinsuke Kodama · Hisashi Otake
Received: 12 November 2009 / Accepted: 17 August 2010 / Published online: 16 October 2010© Springer Science+Business Media B.V. 2010
Abstract The absolute reflectance of the Moon has long been debated because it has beensuggested (Hillier et al. in Icarus 151:205–225, 1999) that there is a large discrepancy be-
M. Ohtake (�) · T. Morota · J. Haruyama · H. OtakeInstitute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshino-dai,Sagamihara, Kanagawa 229-8510, Japane-mail: [email protected]
T. Morotae-mail: [email protected]
J. Haruyamae-mail: [email protected]
H. Otakee-mail: [email protected]
T. Matsunaga · Y. Yokota · S. YamamotoCenter for Global Environmental Research, National Institute for Environmental Studies,16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan
T. Matsunagae-mail: [email protected]
Y. Yokotae-mail: [email protected]
S. Yamamotoe-mail: [email protected]
Y. Ogawa · C. Honda · K. KitazatoThe University of Aizu, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
Y. Ogawae-mail: [email protected]
C. Hondae-mail: [email protected]
K. Kitazatoe-mail: [email protected]
58 M. Ohtake et al.
tween the absolute reflectance of the Moon derived from Earth-based telescopic data andthat derived from remote-sensing data which are calibrated using laboratory-measured re-flectance spectra of Apollo 16 bulk soil 62231. Here we derive the absolute reflectance of thelunar surface using spectral data newly acquired by SELENE (Kaguya) Multiband Imagerand Spectral Profiler. The results indicate that the reflectance of the Apollo 16 standard site,which has been widely used as an optical standard in previous Earth-based telescopic andremote-sensing observations derived by Multiband Imager, is 47% at 415 nm and 67% to76% at 750 to 1550 nm of the value for the Apollo 16 mature soil measured in an Earth-basedlaboratory. The data also suggest that roughly 60% of the difference is caused by the differ-ence in soil composition and/or maturity between the 62231 sampling site and the Apollo16 standard site and that the remaining 40% difference can be explained by the differencebetween the compaction states of the laboratory and the actual lunar surface. Considerationof the compaction states of the surface soil demonstrates its importance for understandingthe spectral characteristics of the lunar surface. We also explain and evaluate data analysisprocedures to derive reflectance from Multiband Imager data.
Keywords Moon · Kaguya · SELENE · Multiband Imager · Reflectance
AbbreviationsA16StS Apollo 16 standard site used by Clementine UVVIS camera as an
optical standard site; located about 10 km west of the Apollo 16landing site. MI or SP or ROLO data of A16StS is denoted as MI orSP or ROLO A16StS. The number after A16StS indicates theobservation number for MI and SP
corrected RLab62231 RLab62231 corrected using the correction factors in Hillier et al.(1999)
Difflab-MI Difference of reflectance spectra between RLab62231 and MIA16StS
Difflab-Ebt Difference of reflectance spectra between RLab62231 andEarth-based telescopic data in Shorthill et al. (1969)
H. TakedaFrontier Plasma Research Center, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino,Chiba 275-0016, Japane-mail: [email protected]
A. IwasakiResearch Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba,Meguro-ku, Tokyo 153-8904, Japane-mail: [email protected]
R. Nakamura · S. KodamaInformation Technology Research Institute, National Institute of Advanced Industrial Science andTechnology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
R. Nakamurae-mail: [email protected]
S. Kodamae-mail: [email protected]
T. HiroiDepartment of Geological Sciences, Brown University, Providence, RI 02912, USAe-mail: [email protected]
Absolute Reflectance of Lunar Surface 59
MIRAI Mineral Reflectance Analyses Instrument at JAXA ISASMLab62231 Reflectance spectra of Apollo 16 bulk soil 62231 measured by
MIRAI but the soil is a different split (portion) of Apollo 16 bulksoil 62231 than RLAB62231
modeled 62231 Modeled reflectance spectra generated from MLab62231 based onthe theoretical model of Hapke (2008)
RLab62231 Reflectance spectra of Apollo 16 bulk soil 62231 measured atRELAB
SPsite Exact location of second SP Apollo 16 standard site observation62231SaS Optical standard site chosen in this study for the MI instrument;
includes the sampling site of Apollo 16 bulk soil 62231. MI data of62231SaS is denoted as MI 62231SaS
1 Introduction
The absolute reflectance of the Moon has long been debated because it has been suggested(Hillier et al. 1999) that there is a large discrepancy between the absolute reflectance ofthe Moon derived from Earth-based telescopic data (Shorthill et al. 1969) and that derivedfrom remote-sensing data obtained by the Clementine UVVIS camera (Nozette et al. 1994).Hillier et al. (1999) proposed a correction factor of 0.53 to fit the Clementine UVVIS cameradata to the Earth-based telescopic data in five Clementine UVVIS camera observation bands(415, 750, 900, 950 and 1000 nm). However, the reason for this large difference is not fullyunderstood yet, and the absolute reflectance of the Moon is still undefined because boththe Earth-based telescopic data and the previous remote-sensing data may contain errors.The errors in the Earth-based telescopic data may have originated in an atmospheric correc-tion, star calibration, and/or instrument calibration, while the errors in the previous remote-sensing data may have originated in a calibration procedure that obtains a normalized re-flectance value by calculating the coefficients necessary to convert the laboratory-measuredreflectance of a mature lunar soil (Apollo bulk soil 62231) to the average reflectance at acalibration-standard site (Eliason et al. 1997) located several kilometers from the samplingsite, which may have a surface structure different from the sampled site (Hillier et al. 1999).Most of the reflectance studies of the Moon based on Clementine UVVIS camera data haveused reflectance values normalized to the laboratory-measured lunar soil reflectance. Thepurpose of this study, therefore, is to define an absolute reflectance value of the Moon from415 to 1700 nm by using Multiband Imager (MI) and Spectral Profiler (SP) data newly ac-quired by SELENE (Ohtake et al. 2008, 2009; Matsunaga et al. 2008) to evaluate the spectralfeatures of the lunar surface. The band assignments for MI are 415, 750, 900, 950, and 1000nm for the visible band (MI-VIS), and 1000, 1050, 1250, and 1550 nm for the near-infraredband (MI-NIR). To accomplish our purpose, we first check the stability and reliability ofthe MI instrument. The aim of this study is not to describe a procedure for deriving SP re-flectance (we are preparing a separate paper for this purpose) but to compare SP data to MIdata derived basically by similar procedures to check the reliability of MI (to check if thereare any responsivity changes during launch).
We will also investigate the cause of the previously mentioned difference between thereal reflectance and the Clementine UVVIS camera data. The absolute reflectance of theMoon will not only reveal the spectral properties of the Moon but also enable us to calibratethe optical instruments used in ongoing and future lunar exploration missions.
60 M. Ohtake et al.
Table 1 Summary of four Apollo 16 standard site observation conditions. Incidence angle, emittance angle,and phase angle of each observation are presented for the center of A16StS in MI-VIS 1000 nm (nadir-lookingimage). The last row indicates the location of the selected Apollo 16 standard site (A16StS) for this studywithin the used images. Pixel numbers on the upper left and lower right of the A16StS rectangle are presentedas x and y axes
1st observation 2nd observation 3rd observation 4th observation
Date (UT) Nov. 19, 2007 Mar. 21, 2008 Sep. 15, 2008 Mar. 12, 2009
Rev. No. (MI rev.) 0503 2008 4175 6375
Incident angle 42.7 16.9 22.1 27.6
Emission angle 18.2 13.1 3.0 3.6
Phase angle 34.6 27.1 25.9 31.2
Apollo 16 standard site location (1725, 1227) (1716, 1212) (573, 2538) (163, 180)
within the used image (1790, 1434) (1781, 1419) (638, 2745) (228, 387)
2 Data
The Apollo 16 standard site (A16StS; all abbreviations defined in this study are listed in thefront matter) used by Clementine UVVIS camera (Eliason et al. 1997) as an optical standardsite is about 2 × 5 km in size and is located about 10 km west of the Apollo 16 landing site.This location has been widely used as an optical standard in previous Earth-based telescopicobservations (Pieters 1999) although the size of A16StS used for the Earth-based telescopewas much larger. Therefore, MI and SP observed A16StS four times simultaneously duringthe nominal and extended SELENE mission periods to check the stability of the instrumentresponse. The dates of the A16StS observations were November 19, 2007 (first observa-tion), March 21, 2008 (second observation), September 15, 2008 (third observation), andMarch 12, 2009 (fourth observation) in UT. The times of the four observations were cho-sen to achieve similar geometric conditions (specifically the phase angle, the angle betweenthe incidence and emission directions) in order to minimize errors caused by photomet-ric correction, a procedure used to determine the reflectance with standard geometry. Thephase angles of the four A16StS observations were 34.6, 27.1, 25.9, and 31.2 (Table 1). Therectangular area within each MI A16StS image was selected to roughly match the A16StSlocation used by the Clementine UVVIS camera (Eliason et al. 1997) and the location inthe second observation is presented in Fig. 1 as a white rectangle. To more precisely de-termine the location of A16StS in MI’s high-spatial-resolution images, we tried to excludeany bright, fresh craters found in the MI images (20 m/pix in visible bands and 62 m/pix innear-infrared bands), which may have caused a change in derived reflectance from A16StS.We used image-based matching to locate A16StS in the MI images because it is more ac-curate for high-spatial-resolution images than latitude- and longitude-based selection usingspacecraft pointing information. All four MI observation data sets for A16StS are used inthis paper, while the second observation data set for SP was selected to compare with MIbecause the second observation occurred under the best temperature conditions for SP de-tectors. A profile of SP data is located in the center of the MI images, and measurementsacross A16StS are indicated as yellow dots (seven points) in Fig. 2. In addition to A16StS,we also derived MI reflectance spectra for the sampling site of Apollo 16 bulk soil 62231(62231SaS; red square in Fig. 3b). The 62231SaS location was determined by matchingApollo images with the MI image according to Muehlberger et al. (1972).
Reflectance spectra of the Apollo 16 bulk soil 62231 measured at the RELAB facility(Reflectance experiment LABoratory) at Brown University http://www.planetary.brown.edu/
Absolute Reflectance of Lunar Surface 61
Fig. 1 Location of MI Apollo 16standard site. The location of theApollo 16 standard site (A16StS)in the second observation(Table 1) is represented as awhite rectangle. Brightness isadjusted to the observedheterogeneity within the standardsite. The area outlined with adashed box is the location ofimage area covered in Fig. 2
Fig. 2 Profile of SP data sets ofthe Apollo 16 standard siteindicated as yellow dots (sevenpoints)
Fig. 3 Location of 62231SaS(red rectangle). a Larger-scaleimage of 62231SaS. Land marksof the landing site are presentedas white arrows. b Close-up of62231SaS indicated as a redrectangle in MI image
relab/ are used in this study to compare to the remote-sensing observations. The measuredgeometry was set to i = 30° and e = 0°, but the sample density for the measurement is notknown. This reflectance spectrum was used to calibrate the Clementine UVVIS camera.
62 M. Ohtake et al.
Reflectance spectra of the same Apollo 16 bulk soil 62231 under different density (poros-ity) conditions, measured by a MIneral Reflectance Analyses Instrument (MIRAI) at JAXAISAS were also used in this study to evaluate the effect of surface density in real lunar re-golith. The measured geometry was set to i = 30° and e = 0°, and a Spectralon was usedas a standard for measurements. The density was changed from 0.811 to 0.933 g/cm3. Tomake the lowest density, we put the soil into the sample holder slowly by gently tapping togenerate a fluffy surface. To make the highest density we vibrated the sample holder verygently two or three times after the soil was placed into the sample holder. The densities werecalculated using the measured volume of the sample holder and its weight before and afterthe sample was loaded. The particle size and/or compositional sorting may have been causedby these sample treatments, so we tried to minimize such sorting and checked photographsof each sample before measuring to ensure the treatment did not cause any change (the meangrain size of the Apollo 16 bulk soil is reported as from 101 μm to 268 μm by Heiken etal. 1973). We also measured the sample several times after similar treatments starting withplacing the sample into the sample holder to check for variations in the reflectance causedby these treatments and the chemical heterogeneity of the sample itself. Similar absorptionfeatures (center wavelength and depth of absorption) for different density conditions (threeMLab62231 spectra in Fig. 8) seemed to suggest that size sorting and compositional hetero-geneity had no major effect on the composition and size sorting.
3 Analytical Methods
The radiance values of A16StS observed both by MI and SP (second observation) werefirst compared after radiometric correction. This comparison used in-flight dark current,flat-field correction factors (flat-field correction is applied only for MI data), and pre-flightconversion factors from instrument DN to radiance. This procedure checked the instrumentequivalence between MI and SP. It is important to compare the radiance between MI andSP because radiance is the most directly derived value with the lowest errors caused byphotometric correction compared with data from nadir observations, which uses SP and the1000 nm band in MI-VIS. After the radiance calculation, the reflectances of each imageand measurements were derived from MI and SP data using solar-irradiance data (Newkurdescribed in Gueymard 2004) and photometric correction by McEwen et al. (1998). Detailsof the MI radiometric data analysis procedures and the pre-flight and in-flight correctionfactors are discussed in Kodama et al. (2010, this issue).
In geometric correction, geometric parameters are calculated by image matching withinMI cubed bands. Basic correction procedures for geometry are described in Ohtake et al.(2008) and details are reported in Hashimoto et al. (2010). All MI reflectance spectra usedin this study were derived based on photometric correction using a digital terrain model(DEM) generated by MI, but a DEM was not applied for SP reflectance because SP is aline-profiling instrument and doesn’t have spatial resolution. The DEMs used to generateimages and spectra in this study are generated based on the same procedures as in Ohtakeet al. (2009) and Hashimoto et al. (2010). Reflectance values for A16StS were derived asaveraged values over the whole A16StS area (Fig. 1) for MI. The reflectance spectra werederived as an averaged value of the seven measurements described in Fig. 2 for SP. Allreflectances used in this study imply “RADF” as described in (Hapke 1993). RADF is a“radiance factor” defined as the ratio of the bidirectional reflectance of a surface to that of aperfectly diffuse surface illuminated at an incidence angle of zero. The location of 62231SaS(average of 6 × 6 MI pixels) is indicated as a red rectangle in Fig. 3 with land marks of thelanding site.
Absolute Reflectance of Lunar Surface 63
Fig. 4 Comparison of radianceof A16StS observed by MI(circle) and the SP radiancespectrum. The data at 1000 nm ofMI-VIS (red circle) and SP(green plus) at 1000 nm matchwell despite the fact that theywere derived by independentinstruments
The reflectance spectra of the Apollo 16 bulk soil 62231 measured at RELAB was down-loaded from the RELAB database (RLab62231). Reflectance spectra of a different splitof the Apollo 16 bulk soil 62231 measured by MIRAI (MLab62231) are averages of fouranalyses under the same density condition (without sample refill). Laboratory-measured re-flectance spectra are usually derived as “REFF” values; therefore, to compare them withremote-sensing data we used corrected values, derived as RADF. REFF is a “reflectancefactor” (also called reflectance coefficient) defined as the ratio of the reflectance of a sur-face to that of a perfectly diffuse surface under the same conditions of illumination andmeasurement.
4 Results
Radiances of A16StS observed by MI and SP are presented in Fig. 4. Photometric correc-tions are not applied in Fig. 4 to completely eliminate possible errors in photometric correc-tion. In Fig. 4, MI data other than MI-VIS 1000 nm contain the change of radiance causedby different viewing angles because the MI-VIS 1000 nm is the only data taken by MI innadir observation conditions comparable to the nadir observation data of SP. Radiances ofMI-VIS 1000 nm and SP 1000 nm are very well matched, and other data of MI and SP matchrelatively well in spite of other MI data containing the effects of different viewing angles.In addition, MI-VIS and MI-NIR 1000 nm data (blue circle just offset from the red dot ofMI-VIS) match relatively well in spite of their slightly different viewing angles (MI-VIS1000 nm is at nadir, but MI-NIR 1000 nm has a 1.9 degree offset from the nadir), whichdemonstrates consistency between the two MI sensors (MI-VIS and MI-NIR) and betweenMI and SP.
We consider these facts (match between MI A16StS and SP A16StS in radiance at1000 nm and match between MI-VIS and MI-NIR) to be evidence that the pre-flight con-version factors used to derive the radiance for both MI and SP have not changed since thepre-flight optical test (in 2004) because it is unlikely that the response of MI and SP wouldchange by the same magnitude. This also means that the responses of the MI and SP instru-ments have not changed much following launch.
Reflectance spectra derived by MI and SP of A16StS, RLab62231 (Pieters 1999),and RLab62231 corrected using the correction factors in Hillier et al. (1999) (corrected
64 M. Ohtake et al.
Fig. 5 a Reflectance spectraderived by MI (four observations)and SP of A16StS. Reflectancespectra of RLab6223 (black line)and the same spectrum sampledto MI bands and corrected usingthe correction factors in Hillier etal. (1999; red line) are presented.b Scaled reflectance spectraderived by MI and SP of theA16StS
RLab62231), which are derived from Earth-based telescope values by adjusting them toRLab62231, are presented in Fig. 5a and in Table 2. Scaled reflectances of the same spec-tra relative to 750 nm are presented in Fig. 5b. Four MI data sets of A16StS match well,indicating that no significant response change occurred in the MI instrument during thoseobservation periods. Response stability of SP is also confirmed (in preparation), which in-dicates that SP data taken in different time periods are distributed in the same photometricfunction curve. Comparing the MI and SP reflectance data indicates that they agree relativelywell in the MI observation wavelength range, demonstrating no significant response changein either instrument in this wavelength range though the reflectance data differ slightly upto 0.8% in absolute reflectance. The reason for this difference is not clear at present, butwe presume this may be caused by different spatial resolution (surface roughness effectsincluding local topography) and photometric correction errors as discussed later.
Figure 5a demonstrates that the MI A16StS 1 to 4 and SP A16StS are much lowerthan RLab62231. We call the difference of reflectance spectra between MI A16StS andRLab62231, Difflab-MI. MI A16StS and SP A16StS are also noticeably higher than the cor-rected RLab62231 (Hillier et al. 1999), except at 415 nm where it is only slightly lower(<1% in absolute reflectance) than the corrected RLab62231. The reflectance derived by MIis 45% of the RLab62231 reflectance at 415 nm and 70 to 75% at 750 to 1550 nm (Table 2).
Absolute Reflectance of Lunar Surface 65
Table 2 Reflectances of MI A16StS, SP A16St, RLab62231, corrected RLab62231, and MI 62231SaS withratios of MI A16StS/RLab62231 and MI 62231SaS/RLab62231. Describing the correction factors for SP isbeyond the scope of this paper, and the SP A16StS values may change in the near future as we keep improvingSP data calibration and correction
RADF RADF RADF RADF RADF RADF ratio RADF ratio
Wavelength(nm)
MIA16StS(obs2)
SPA16StS(obs2)
RLab62231
Corr.RLab62231byHillierfactor
MI62231SaS(6 × 6 pix.)
MIA16StS/RLab62231
MI62231SaS(6 × 6 pix.)/RLab62231
415 0.044 – 0.093 0.050 0.062 0.474 0.665
750 0.103 0.096 0.153 0.082 0.133 0.673 0.866
900 0.115 0.110 0.164 0.087 0.145 0.704 0.887
950 0.122 0.120 0.168 0.089 0.151 0.725 0.897
1000 0.127 0.124 0.173 0.092 0.156 0.731 0.897
1050 0.131 0.132 0.180 0.096 0.159 0.725 0.881
1250 0.149 0.155 0.204 0.108 0.177 0.730 0.869
1550 0.179 0.183 0.235 0.125 0.208 0.762 0.885
In Fig. 5a, reflectance lines of MI A16StS data (four observation lines) and that of corrected(Hillier et al. 1999) RLab62231 (red line) crossed around 450 nm. This may suggest that, at450 nm, MI A16StS data is consistent with the Earth-based telescopic data used in Hillier etal. (1999) because the authors used 445 nm reflectance values of the Earth-based telescopicdata to generate correction factors. We also compare MI data to ROLO (ROLO: USGS Ro-botic Lunar Observatory) reflectance (Staid and Stone 2007) of A16StS. ROLO reflectancematches MI A16StS very well, though we took the ROLO reflectance number from theabstract (Staid and Stone 2007). The differences between MI A16StS and ROLO A16StSare less than 0.4% in absolute value except at 415 nm where ROLO reflectance is slightlyhigher (2% in absolute value) than MI. The fact that the corrected RLab62231 (which corre-spond to reflectance of A16StS determined by Earth-based telescopic data), ROLO A16StSand MI A16StS match well demonstrates compatibility of MI and Earth-based telescopicreflectances.
In Fig. 5b, the MI A16StS and SP A16StS data are redder than RLab62231 data, possiblydue to different mineral components and/or degrees of space-weathering (and/or differencesin other parameters, such as grain size) between A16StS and RLab62231. The SP data arealso redder than MI A16StS data. The reason for this is not currently clear, but two possi-bilities are spatial resolution (the surface roughness effect including local topography) andphotometric correction errors. The slight response change in MI-NIR (difference betweenMI A16StS 1 and MI A16StS 2–4) is also a contributing factor. If this discrepancy in re-flectance in visible and near-infrared wavelength and slope between MI A16StS and SPA16StS is caused by different spatial resolutions, we probably can’t correct entirely; how-ever, at least our estimations of absolute reflectance of the lunar surface (e.g., A16StS and62231SaS) are valid in MI spatial resolution and we can use the MI correction factors. How-ever, if this discrepancy is caused by photometric correction, in future studies we may beable to better correct the reflectance derived by MI, though in the present study, we usedthe best photometric correction available (McEwen et al. 1998). Even with uncertainty up to8% in reflectance (which corresponds to the maximum difference between MI and SP), we
66 M. Ohtake et al.
Fig. 6 Comparison of MI andthe Earth-based telescopic data ofTycho crater (with 0.2 offset). MIdata are averaged to a similarspatial resolution (5 km) ofEarth-based telescopes, andpre-flight conversion factors areused in this figure even thoughthe exact observed area of theEarth-based telescopic data isunknown (spatial resolution is 3to 10 km). Data are scaled at1000 nm for MI. The Earth-basedobservation reflectance spectraare from http://pds-geosciences.wustl.edu
believe that our discussion on the difference between laboratory-measured Apollo 16 bulksoil and remote sensing data is still valuable, because their difference is as large as 50%.
Estimating the size of errors within the MI-derived absolute reflectance is difficult be-cause we do not have in-situ ground truth data of the Moon. Earth observation satellitescommonly use simultaneously observed ground-based spectral data as a calibration stan-dard, but we do not have this kind of data for the Moon. The Apollo sample data may notbe sufficient because of the spatial resolution difference between the centimeter-scale sam-ple collection and the remote-sensing data as well as differences in micro-texture betweennatural in-situ measurements and measurements of lunar samples in Earth-based laborato-ries. Despite these restrictions, we estimated the absolute reflectance error. The radiometriccalibration error estimated based on the pre-flight optical test is less than ±0.7% (Kodamaet al. 2010, this issue). Though we can’t determine exact errors after the launch, the factthat the pixel-to-pixel sensitivity variation between in-flight cycles is less than ±0.5% (Ko-dama et al. 2010, this issue) suggests that the remaining error after applying in-flight flatfield calibration (which is meant to calibrate pixel-to-pixel sensitivity variation) can be esti-mated as less than ±0.25% within one-band images (though errors among MI-band imagesmay be slightly larger). The error caused by photometric correction is assumed to be lessthan ±1.5% from the variation of MI A16StS data among observations taken during dif-ferent periods (Fig. 5) for a phase angle ranging from 19 to 36 degrees, but this error maydiffer in a wider phase angle range (photometric correction error in a wider range is animportant scientific issue but beyond the scope of this study). The total estimated error ofMI-derived absolute reflectance of A16StS is therefore less than ±2.0% from a calculationof (0.72 + 0.252 + 1.52)0.5 (though errors among MI band images may be slightly larger).
To test the spectral reliability of the MI data, we compare Earth-based telescopic re-flectance measurements to MI data (MI data are averaged to match the spatial resolution ofEarth-based telescopes and pre-flight conversion factors are used in this figure) at Tycho inFig. 6 (reflectance in the figure is presented as a scaled value because available digitizedEarth-based telescopic reflectances are provided only as scaled values). The central peakand floor spectra agree well in absorption center wavelength and spectral shape, though asmall spectral correction may be required in MI data as described later.
Reflectances of individual MI pixels within the A16StS area vary in absolute values from9 to 13% at 750 nm (Fig. 7a). The majority (around 80%) of the areas have a reflectanceof 10.5% (Fig. 7b) with standard deviation of 0.18 to 0.39%. The locations of the exact SP
Absolute Reflectance of Lunar Surface 67
Fig. 7 a Reflectance within theA16StS. Reflectances within theA16StS area vary from 9 to 13%at 750 nm at MI’s spatialresolution. b Variation ofreflectance within the A16StS.Numbers of pixels of eachreflectance within the A16StS arepresented in log scale
observation (SPsite) and of A16StS differ slightly (about 2 km in the longitude direction),but the effect of this difference is negligible as demonstrated in the MI A16StS and MISPsite data, which are averages of MI data of the exact SP observation locations in Fig. 2.
Figure 8a and b indicate the correlation between MLab62231 under different densityconditions as discussed above, the averaged absolute reflectance spectra of MI A16StS, andMI 62231SaS (the 62231SaS location was presented in Figs. 3 and 10). The MI 62231SaSreflectance is significantly lower than RLab62231 reflectance (ratios of MI 62231SaS toRLab62231 in different MI observation bands vary from 0.67 to 0.89 as listed in Table 2in the left-most column), and it is higher than MI A16StS. The ratios of MI A16StS toRLab62231 in different MI observation bands vary from 0.47 to 0.76 as listed in Table 2in the second column from the left. The reflectance change caused by the density change is25% of the absolute reflectance (between density 0.933 and density 0.811) in the measureddensity range. Figure 8b demonstrates the slope of the MLab62231 became redder with de-creasing sample density. Therefore, we interpret the fact that MI A16StS and MI 62231SaSare both redder than RLab62231 is due to the density of the lunar surface being lower thanthat in the laboratory measurements.
68 M. Ohtake et al.
Fig. 8 a Reflectance spectra oflaboratory-measured 62231 andMI data. Reflectance ofRLab62231, MLab62231 underthree density conditions, modeled62231, the averaged absolutereflectance spectra of MIA16StS, and MI 62231SaS arepresented. The modeledreflectance spectra withreflectance at 750 nm matchingMI 62231SaS are presented as ared line. The estimated fillingfactor of the modeled reflectancespectra was 0.13, correspondingto a bulk density of 0.4 g/cm3.b Scaled reflectance spectra oflaboratory-measured 62231 andMI data. The slope of thereflectance spectra increases withdecreasing filling factors. Noisearound 850 nm is caused bydetector switching at thiswavelength in MIRAImeasurements
RLab62231 reflectance spectra indicate a shallow absorption feature centered around950nm, while the MI 62231SaS data have no clear features. The reason for this differencemay be one or more of the following: (1) the small response change after the pre-flightoptical test, (2) calibration errors in MI data, (3) the effect of different mineralogy and/ormaturity in different spatial resolutions (120 m square in the MI 62231SaS (6 × 6 pixels)data), and (4) the density difference between the lunar surface and the laboratory sample.We do not believe that effects (1) and (2) are likely because of the similarity of the modeledreflectance spectra of 62231 (modeled 62231), as described in detail in a later section.
There is also a slightly different reflectance value (up to 0.5%) between the two typesof laboratory reflectance measurements from 500 nm to 900 nm, but a weak feature near1 μm itself (at wavelengths exceeding 900 nm) matches well between the two types of lab-oratory measured reflectance. Spectra of olivine from the same location (San Carlos, AZ)determined by two laboratory measurements match relatively well (Fig. 12 in Appendix),indicating basic compatibility between the two laboratory instruments. This basic compat-ibility of the two laboratory instruments and the slight difference in the Apollo bulk soil62231 reflectance between the two laboratory instruments may suggest a slight increase ofsmaller particles in our laboratory measurements (MIRAI data) than in RELAB data.
Absolute Reflectance of Lunar Surface 69
Fig. 9 Variation of reflectancewithin 62231SaS
The variation within the decided 6×6 pixels of MI 62231SaS is relatively small (standarddeviation is 0.16 to 0.39%; Fig. 9), and therefore the errors caused by the determination errorof the sampling-site location are believed to be small.
5 Density Effects Hypothesis on Measurement of Soil Spectra
The cause of the difference between RLab62231 reflectance spectra and that the reflectancespectra derived from Earth-based telescopic data in Shorthill et al. (1969) (Difflab-Ebt) wassuggested in previous works to correspond to a difference of roughness and compactionstates between the laboratory-measured samples and those of the actual pristine lunar sur-face (Hillier et al. 1999). However, the effect of compaction states has not been quantitativelyevaluated, nor has it been determined that this is the sole cause of Difflab-Ebt because a the-oretical model of the compaction states had not been available until recently (Hapke 2008)and because of the lack of new and possibly representative remote-sensing data from theApollo 16 landing site. As described in the results section, our data was obtained at a higherspatial resolution, and the response reliability was checked and confirmed. Therefore, wemay be able to discuss the cause of Difflab-Ebt by using MI data.
If we assume (i) soil characteristics (composition, maturity, and grain size) of Apollobulk soil 62231 is representative of 62231SaS, and (ii) MI reflectance (MI A16StS and MI62231SaS) derived by the pre-flight correction coefficient is reliable at least at 750 nm, therelationship among MI A16StS, MI 62231SaS, and RLab62231 indicates that the Difflab-MI
(which corresponds to the difference between RLab62231 and MI A16StS in Fig. 8a) ispartly (roughly 60%) attributed to differences in soil characteristics such as compositionand maturity between 62231SaS and A16StS (Difflab-MI are reduced by 60% if we use MI62231SaS instead of A16StS).
Again, if we assume soil characteristics (composition, maturity, and grain size) of Apollobulk soil 62231 is representative of 62231SaS, the remaining 40% difference in Difflab-MI
(which correspond to the difference between RLab62231 and MI 62231SaS) should becaused by other parameters that differ between the lunar surface and the laboratory suchas sample density (compaction states) and/or surface roughness. We hypothesized that theremaining 40% can be explained by the difference of density (compaction states) between
70 M. Ohtake et al.
Fig. 10 Color-composite imagearound A16StS and 62231SaS.a A16StS is represented as awhite rectangle. The image areacovered in b is enclosed within adashed box. b Close up of62231SaS (red rectangle)
the laboratory (RLab62231 or MLab62231) and the actual lunar surface (MI 62231SaS).We selected the density as the cause of the remaining 40% because, judging from the pho-tograph of Apollo 16 station 2 (which is the sampling site for Apollo bulk soil 62231)taken by the Apollo astronauts, there is no positive evidence that suggests anomalous sur-face roughness of the site (lunar surface) compared to the laboratory measurements (weexclude large-scale roughness effects such as tenths of meters because basically that effectwas removed by adopting photometric correction including local topography). The densitychanges easily between the site (lunar surface) and laboratory because of gravity, electrosta-tic charge, and micrometeorite impact effects. Also, the density effects on the soil spectracan be large enough to explain the observed remaining 40% difference according to previousqualitative analyses (Ohtake et al. 2003). From the fact that MI A16StS and the Earth-basedtelescopic data (Hillier et al. 1999; Staid and Stone 2007) matches well as described previ-ously, Difflab-MI and Difflab-Ebt may be suggested to have similar causes. Though our data andunderstanding of optical properties of lunar soil are currently limited, we believe the densityis one plausible explanation as described above.
Clementine UV/VIS camera reflectances were derived by applying conversion factors toconvert observed signals to generated reflectances assuming that reflectances of A16StSobserved by the Clementine UV/VIS camera and RLab62231 are the same. Therefore,Clementine UV/VIS camera reflectance data may contain a discrepancy between A16StSand RLab62231 (Difflab-Ebt) as described above. Our intention to discuss reflectance of theClementine UV/VIS camera is not to point out the limitations of the very useful and impor-tant previous work by Clementine UV/VIS camera but to understand the actual lunar surfacereflectance.
6 Correction Method to Derive MI Reflectance
6.1 Selection of an Optical Standard Site
For an Earth-based telescope that is relatively poor in spatial resolution, it is best to avoidheterogeneous locations. Nonetheless, the composition of the Apollo 16 bulk soil 62231 andA16StS may differ judging from the substantial reflectance difference between MI A16StSand MI 62231SaS in Fig. 8. In contrast, the spatial resolution of MI is much higher thanthat of the Earth-based telescopes, so we can attempt to identify and use the exact samplingsite as an optical standard site to minimize the effects due to possible compositional and/ormaturity differences between Apollo 16 bulk soil 62231 and A16StS.
Absolute Reflectance of Lunar Surface 71
From the absorption depth map (Fig. 10) around A16StS and 62231SaS, MI A16StS(partly orange and partly green) and MI 62231SaS (mainly blue) appear to differ in mineral-ogy and/or maturity, and the bluish color of MI 62231SaS is possibly more representative ofthe plagioclase-rich mineralogy of Apollo 16 bulk soil 62231 (http://web.utk.edu/~pgi/data.html: Lunar Soil Characterization Consortium). This bluish appearance of 62231SaS re-sembles that of the South Ray crater ejecta and Buster crater (though the Buster crater isbarely recognizable in the MI image) and possibly matches the geologic interpretation of62231SaS (Apollo 16 station 2) by Muehlberger et al. (1972) (they interpreted the area asbeing covered by South Ray crater ejecta or Buster ejecta or both).
The lower maturity (lower slope) of RLab62231 compared to MI A16StS and the similarmaturity of RLab62231 and MI 62231SaS also may support similar composition and/or sim-ilar maturity of Apollo 16 bulk soil 62231 and 62231SaS and different mineral componentsand/or space-weathering degrees between A16StS and RLab62231. Moreover, we prefer62231SaS over A16StS as a standard site because both RLab62231 and MLab62231 clearlyhave much higher reflectances than A16StS (which is consistent with the redder spectra ofA16StS). It may also mean that RLab62231 and MLab62231 have stronger spectral featuresthan A16StS. Therefore, if we use MI A16StS as an optical standard site we may be enhanc-ing (or over printing) weak spectral features of the actual MI A16StS spectra by adjustingto the stronger spectral features (lower maturity) of RLab62231, MLab62231, or modeled62231. A relatively small variation of MI derived reflectance within 6 × 6 pixels around62231SaS may also allow us to use this site (62231SaS) as an optical standard site for MI.
Though MI A16StS indicates a more mature spectra than MI 62231SaS, and small vari-ations in the development of soil components (maturity) affect the spectra, maturity has agreater effect in lowering the reflectance or in changing the slope than in changing spectralfeatures (absorption center and absorption width) near 1 μm band caused by mafic minerals.In contrast, compositional differences also have at least similar (and possibly greater) effectson spectral features (absorption center and absorption width) than maturity. Because the ab-solute reflectance of MI derived by pre-flight correction coefficients is reliable (as describedin this paper) and because we can minimize the effect of errors in absolute reflectance bycontinuum removal, we believe that we should concentrate on selecting a standard site withminimum compositional differences from the available Apollo soil samples.
Based on the above facts, we believe that 62231SaS is better than A16StS for MI, al-though this site may not suit other instruments because the preferred standard site dependson each instrument’s specifications and observation conditions (for example, site selectionmay depend on spatial resolution, responsivity change after launch, spatial coverage and soon).
6.2 Derivation of MI Correction Coefficient
Our evaluation demonstrated that MI’s response basically did not change (at least at 750 nm)and that we can therefore rely on MI reflectance data at 750 nm using pre-flight correctionfactors. However, judging from the slight difference between RLab62231 (and MLab62231)and MI 62231SaS in Fig. 8, a minor correction in reflectance relative to wavelength is re-quired. To make this minor correction, we derived correction factors relative to the MI re-flectance at 750 nm by calculating the adjusting factors to fit the MI 62231SaS average re-flectance derived using a pre-flight correction coefficient to the modeled 62231 (red line inFig. 8). The reflectances of modeled 62231 used here, the derived correction factors for MI,and the ratios of corrected MI A16StS and RLab62231 spectra are presented in Table 3. Theratios of corrected MI A16StS and RLab62231 spectra are the correction factors we derived
72 M. Ohtake et al.
Table 3 Reflectances of the modeled spectrum, the derived correction factors for MI, and the ratios ofcorrected MI A16StS and RLab62231 spectra
RADF Factor RADF ratioWavelength(nm)
Modeledspectra(ϕ = 0.13)
Correctionfactor for MIbands usingMI62231SaS(6×6 pixels)(relative to750 nm)
MI A16StS(corrected)/RLab62231
415 0.083 1.344 0.637
750 0.132 1.000 0.673
900 0.147 1.016 0.716
950 0.151 1.006 0.729
1000 0.156 1.009 0.738
1050 0.163 1.032 0.749
1250 0.187 1.062 0.775
1550 0.216 1.045 0.797
for the Clementine UV/VIS data and range from 0.64 (at 415 nm) to 0.80 (at 1550 nm). Weused modeled 62231, which is generated from MLab62231, to match to the MI reflectancedata at 750 nm (0.133 at 750 nm in MI 62231SaS) by changing porosity (density) basedon the hypothesis that 40% of Difflab-Ebt is caused by a difference of density (compactionstates) between the laboratory sample and the actual lunar surface. The modeled 62231 wasused here instead of RLab62231 or MLab62231 to reproduce the slope of actual 62231SaSspectra because the slope of the reflectance spectra increases with decreasing filling factors(Fig. 8b).
To derive the modeled 62231 by changing the porosity (which is described by 1 − �,where � is the filling factor), we applied the recently proposed theoretical model of Hapke(2008) to MLab62231. The estimated filling factor of the modeled 62231 (red line in Fig. 8),which we generated from the reflectance of MLab62231 with a density of 0.811 (darkblue line in Fig. 8), corresponds to a bulk density of 0.4 g/cm3, assuming 3.1 (Duke etal. 1970) as the specific gravity of the material. The derived modeled 62231 and the MI62231SaS derived using pre-flight correction coefficients also match well, not only at 750but up to 1000 nm, demonstrating again that no response change had occurred in these wave-lengths since the pre-flight optical test. In the 1050, 1250, and 1550 nm bands, however, MI62231SaS is lower (3.8 to 6.7%) than the modeled 62231, possibly due to a slight responsechange in the MI-NIR instrument during launch and/or operation considering the slight dif-ference between the first MI A16StS (MI A16StS 1) and three other observations (A16StS2–4) as presented in Fig. 5a (difference between MI A16StS 1 and average of MI A16StS2–4 is up to 3.5%). The reflectance difference at 415 nm between the modeled 62231 andMI 62231SaS exceeds the difference at near-infrared wavelengths (i.e., at 1050, 1250, and1550 nm).
Since the corrected RLab62231 (red line in Fig. 5a), calculated using correction fac-tors based on Earth-based telescopic data of the Moon (Hillier et al. 1999), matches thereflectance at 415 nm in MI A16StS well, it is not likely that this difference at 415 nm iscaused by instrument errors. Therefore, we consider that this difference may be caused byspace weathering (Pieters et al. 1993) which caused reddening of the spectra because the
Absolute Reflectance of Lunar Surface 73
Fig. 11 a Reflectances of fiverepresentative Apollo 16 bulksoil samples. b Scaledreflectances of five representativeApollo 16 bulk soil samples
actual top layer of the lunar surface likely suffers more severe space weathering than re-turned Apollo soil samples, which are mixtures of several centimeters depth of lunar surfacesoil. However, this difference is also possibly caused by errors in the photometric functioncorrection and/or modeled spectra at this wavelength.
MLab62231 at a similar density (around 0.811) change by up to 2% in absolute valueat 750 nm in our laboratory because of heterogeneity in the material, grain size, and spaceweathering degree of the soil samples. Therefore, the estimated filling factor is affectedby both this heterogeneity and the compaction effect. From our estimation, the estimatedfilling factor for MI 62231SaS ranges from 0.13 to 0.26 (and thus from 0.4 to 0.8 in bulkdensity). These values are lower than the previously estimated filling factor of 0.5, whichcorresponds to a bulk density of 1.3 to 1.6, for the top 15 cm surface of the regolith (Duke etal. 1970; Christensen et al. 1967; Mitchell et al. 1974). This may suggest the possibility thatthe topmost layer of the surface (possibly a few millimeters) of the lunar regolith is moreporous than the deeper layers.
There is a slight difference of reflectance from 500 nm to 900 nm between RLab62231and MLab62231 (the maximum difference is 0.5% in absolute value) but a weak featurenear 1 μm (at wavelengths exceeding 900 nm) is highly consistent. We need more study
74 M. Ohtake et al.
to understand the cause of this 0.5% difference between the two laboratory instruments.However, we still prefer to use the modeled 62231 to derive reflectance because of thecompatibility of the two laboratory instruments (Fig. 12 in Appendix) and because there isa density effect on reflectance which is known to exist and which apparently exceeds theinter-laboratory difference.
We will apply these correction factors (Table 3) in the nominal MI data-production pro-cedure that will be used to generate files open to the public to derive reflectances, althoughthese correction factors may be changed in the future with progress in spectral studies ofthe lunar soil. We estimated color ratio errors between 750 nm and other bands as < ±1%from the variations of four A16StS data sets. Apollo bulk soil 62231 was used here to derivecorrection factors because this soil is one of the most mature (space-weathered) sample ofthe five representative soil samples collected in the Apollo 16 mission (Fig. 11). This sampleenables us to avoid errors caused by heterogeneity around the sampling site and errors ofdetermining the sampling site. Mature soil is more mixed with nearby materials because ithas been exposed longer on the lunar surface and has suffered more cratering processes thanfresh (less mature) soil. Therefore, mature soil is preferable for minimizing the effects ofsmall-scale heterogeneity of the geologic settings of the sampling sites of the standard lunarsoil. Also, this soil is the most extensively studied (Pieters 1999; Ohtake et al. 2003), andits spectral characteristics are (relatively) well known. We understand that our current cor-rection and calibration procedure may not be perfect. Therefore, we consider its importancein maintaining the ability to compare our results to other remote sensing data by providinginformation of our correction and calibration procedure; and if refinement is necessary, wehope to do so in the near future.
Figure 13 (see Appendix) presents the schematic relationships among discussed re-flectance values and corresponding observation locations with the basic idea for MI re-flectance correction.
7 Conclusions
No response change occurred in the MI-visible bands (415, 750, 900, 950, and 1000 nm)since the pre-flight optical test, but small changes may have occurred in the near-infraredbands. In the nominal MI data-production procedure that will be used to make the files opento the public, we adopt the reflectance at 750 nm using a pre-flight correction coefficient.For other bands we apply the correction factors derived by adjusting MI 62231SaS to themodeled 62231 (Table 3).
From our results, we hypothesize that the causes of the difference between Earth-based telescopic data and those derived from the Clementine UVVIS camera (namely,the Clementine-derived reflectance is almost twice as large as the Earth-based telescopicdata) are: (1) different material (soil composition and/or maturity) between A16StS and62231SaS, which caused roughly 60% of the difference, and (2) different surface porosi-ties (densities) between the laboratory sample and the actual lunar surface, which may havecaused the remaining 40% of the difference.
There are still issues remaining to be studied, but, based on this study, we are confidentthat the stability and reliability of MI data are sufficient, and we hope that the MI-generatedproducts that will be made available to the public will contribute to future lunar research.
Acknowledgements We thank SELENE project team members Y. Takizawa, S. Sasaki, M. Kato, H. Mizu-tani, K. Tsuruta and R. Nagashima. We also thank Fujitsu Limited engineers T. Maekawa, K. Tsubosaka,N. Tonoya, J. Inoue, N. Masuda and T. Nakashima. We are grateful to Mitsubishi Space Software Co. Ltdengineers M. Hashimoto, K. Torii, Y. Kurashina, A. Yoshizawa and S. Nakanotani. The long-term efforts byeach of these teams were essential to our work.
Absolute Reflectance of Lunar Surface 75
Appendix
Fig. 12 Olivine reflectancespectra of the two laboratoryinstruments (RELAB andMIRAI). Spectra of the twolaboratory instruments matchrelatively well, indicating basiccompatibility between the twolaboratory instruments. However,the grain sizes of these samplesdiffer slightly (the RELABolivine sample was sieved asfrom 0 to 250 μm, but the grainsize of MIRAI olivine sample issieved at 75 to 105 μm), and thespectra of olivine samples fromSan Carlos may differ slightlydue to small amounts ofinclusions in olivine
Fig. 13 Schematic relationship among discussed reflectance values. Each described reflectance and corre-sponding observation location with basic idea for MI reflectance correction are presented
76 M. Ohtake et al.
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